Are you using carrierwave for your images uploads? You can store them on amazon S3 reasonably easy with carrier wave. Carrierwave instructions Other solutions have S3 storage easily accessible as well.

Heroku will NOT let you store files in the filesystem. Run

RAILS_ENV=production bundle exec rake assets:precompile

to compile you assets locally, add to git, and push to heroku but you cannot add images later via your application on heroku. If you upload them to the /temp folder they will stay there for a short while or until you re-deploy/update your code I believe.